FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES

Authors : Sun Young JANG, Choonkil PARK

Pages : 711-723

View : 12 | Download : 5

Publication Date : 2011-05-01

Article Type : Research Paper

Abstract :The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Th. M. Rassias introduced the following equality Xm i,j=1 kxi − xjk 2 = 2m Xm i=1 kxik 2 , Xm i=1 xi = 0, for a fixed integer m ≥ 3. By the above equality, we define the following functional equation insert ignore into journalissuearticles values(0.1); Xm i,j=1 finsert ignore into journalissuearticles values(xi − xj ); = 2m Xmi=1 finsert ignore into journalissuearticles values(xi);, Xm i=1 xi = 0. In this paper, we prove the generalized Hyers-Ulam stability of the functional equation insert ignore into journalissuearticles values(0.1); in fuzzy Banach spaces.
Keywords : Fuzzy Banach space, Functional equation related to inner product space, Generalized Hyers Ulam stability, 2000 AMS Classification 46 S 40